1. Field of the Invention
The present invention relates to a method and apparatus for equalization by compensating for a wave distortion caused by intersymbol interference in digital communication such as mobile radio communication.
2. Description of the Related Art
A maximum likelihood sequence estimation (MLSE) is known as one of adaptive equalizers. In this equalizer, likelihood functions corresponding to all possible signal sequences are calculated, and a signal sequence maximizing the likelihood function is selected in signal decision. However, with an increase in length of a signal sequence, the number of all possible signal sequences is exponentially increased. A Viterbi equalizer which estimates states by using a Viterbi algorithm is known as an equalizer capable of reducing the amount of arithmetic processing by decreasing the number of signal sequences G. D. Forhey, "Maximumlikelihool sequence estimation of digital sequences in the presence of intersymbol interference," IEEE Trans. Inform. Theory, Vol. IT-18, pp. 363-378, May 1972.
FIG. 1 is a block diagram showing the arrangement of a conventional Viterbi equalizer. (A. Baier, G. Heinrich, and U. Wellens, "Bit Synchronization and Timing Sensitivity in Adaptive Viterbi Equalizers for Narrowband-TDMA Digital Mobile Radio Systems", Proc. IEEE Vehicular Technology Conference '88, pp. 377-384, June 1988).
Referring to FIG. 1, a quasi-coherent demodulated signal is input to a sampling circuit 111 through an input terminal 10. The sampling circuit 111 outputs a sampled signal to a correlator 11 and a subtracting circuit 12. A sampled signal y(i) is a sampled value of the quasi-coherent demodulated signal when a received signal r(t) is represented by EQU r(t)=Re[y(t).multidot.exp(j2.pi.ft)] (1)
where f is the carrier frequency, and Re [x] is the real part of x. In this case, assume that the sampled signal y(i) includes a modulation wave having a symbol rate 1/T, and the sampling frequency is represented by T.
The correlator 11, which receives the sampled signal y(i), estimates the impulse response of radio transmission on the basis of a known signal included in a transmitted signal. For example, the impulse response of radio transmission can be estimated by calculating correlation of the sampled signal with a training signal added to the start portion of a burst (as shown in FIG. 2). The correlator 11 sets this estimated impulse response value as the tap coefficient of a transversal filter 13. Note that the tap coefficient is not updated in a data signal interval of the burst.
The subtracting circuit 12 subtracts a transversal filter output from the sampled signal y(i) and outputs the resultant value as an estimation error. A squaring circuit 110 multiplies the square of the estimation error by -1 and outputs the resultant value, as a branch metric, to a Viterbi algorithm circuit 15 through a switch circuit 14. In the Viterbi algorithm circuit 15, a finite number of state transitions occur every period T. In this case, four types of state transitions are exemplified. Code sequences corresponding to the respective state transitions are input to a signal generating circuit 16. The signal generating circuit 16 generates complex symbol signal sequences corresponding to the respective input code sequences. The switch circuit 17 sequentially selects the signal sequences and outputs them to the transversal filter 13. The transversal filter 13 has a tap coefficient common to all the state transitions. The transversal filter 13 converts the signal sequences, which differ from each other in the respective state transitions, into estimated signals, and outputs them. Note that if a complex symbol signal sequence coinciding with a transmitted one is input to the transversal filter 13, an estimated signal nearly equal to the received signal is output. The switch control circuit 18 controls a switch circuit 14 and the switch circuit 17 at the same timing.
The output of the squaring circuit 110 is identified as a branch metric of a state transition selected by the switch circuit 14, and is input to the Viterbi algorithm circuit 15. The Viterbi algorithm circuit 15 performs signal decision, and outputs the resultant decision signal from an output terminal 19.
A Viterbi algorithm for state estimation will be described below with reference to BPSK (binary phase shift keying) modulation. The sampled signal y(i) in a multipath propagation can be represented as follows: ##EQU1## where K is a positive integer, h(i) is the impulse response, a(k) is the complex symbol of a BPSK signal, which assumes "+1" or "-1" according to the transmitted data, and n(i) is white Gaussian noise. In equation (2), h(i) represents the impulse response of a two-path model. If the time spread of this impulse response is represented by 1T, then ##EQU2## Since intersymbol interference is caused, the sampled signal y(i) is obtained by weighting a(i) and a(i-1) by h(0) and h(1), respectively, and combining the weighted values and n(i). In this case, the radio transmission is described in two states. Note that the radio transmission is represented by using two states when the time spread of the impulse response is given by 1T. In general, when the spread is represented by (K-1)T, the constraint length is given by K, the radio transmission is described in 2.sup.K-1 states. Assume that sth state at a time point i-1 is represented by .sigma..sup.s.sub.i-1. In this case, since 0.ltoreq.s.ltoreq.1, states .sigma..sup.0.sub.i-1 and .sigma..sup.1.sub.i-1 appear. When the time point advances from (i-1) to i, state transition occurs. Since a transition is dependent on the value of a complex symbol candidate .alpha.(i)=.+-.1, two types of state transition occur from one state. Since the transition is destined for .sigma..sup.0.sub.i or .sigma..sup.1.sub.i, the trellis diagram shown in FIG. 3 is obtained. As shown in this diagram, one state branches into two states, and two states merges into one state. That is, .sigma..sup.0.sub.i is the transition destination when .alpha.(i)=-1, and .sigma..sup.1.sub.i is the transition destination when .alpha.(i)=1. In order to select one of two transitions merging at a transition destination, a transition metric J.sub.i (.sigma..sup.s.sub.i,.sigma..sup.s'.sub.i-1) corresponding to a transition from .sigma..sup.s.sub.i to .sigma..sup.2'.sub.i-1 is used.
A transition metric for the transition from the state .sigma..sup.1.sub.i to the state .sigma..sup.s'.sub.i-1 is calculated by using a branch metric BR(.sigma..sup.s.sub.i, .sigma..sup.2'.sub.i-1) for each transition according to the following equation: EQU J.sub.i (.sigma..sup.s.sub.i, .sigma..sup.s'.sub.i-1)=J.sub.i-1 (.sigma..sup.s'.sub.i-1)+BR(.sigma..sup.s.sub.i, .sigma..sup.s'.sub.i-1)(4) EQU For EQU BR(.sigma..sup.s.sub.i, .sigma..sup.s.varies..sub.i-1)=-.vertline.y(i)-{h.sub.0 .alpha.(i)+h.sub.1 .alpha.(i-1)}.vertline..sup.2 ( 5)
where J.sub.i-1 (.sigma..sup.s'.sub.i-1) is the path metric of .sigma..sup.s'.sub.i-1 at the time point (i-1), which corresponds to a likelihood function. A transition signal sequence at the state transition from .sigma..sup.s.sub.i to .sigma..sup.s'.sub.i-1 {.alpha.(i-1),.alpha.(i)}, its elements .alpha.(i-1) and .alpha.(i) are a complex symbol candidate of a(j-1) corresponding to the state at the time point (i-1) and a complex symbol candidate of a(i) corresponding to the transition, respectively. In the Viterbi algorithm, the transition metrics J.sub.i (.sigma..sup.s.sub.i,.sigma..sup.s'.sub.i-1) corresponding to two transitions which merge together are compared with each other, and a transition with a larger transition metric is selected, and the transition metric of the selected transition is set as a path metric J.sub.i (.sigma..sup.s.sub.i) at the time point i. Because only states sequences (paths) linked with selected transitions are left as maximum likelihood sequence candidates, the same number of paths as one of states survive. These paths are called survivor paths. If all the survivor paths merge together at a given past time point, since the state at the time point can be determined, signal decision is performed. If, however, they do not merge, signal decision is postponed. Subsequently, this operation is repeated. Note that if the sequences of states are only stored up to a past time point (D-K+1)T because of limitations imposed on a memory, and survivor paths at the past time point (D-K+1)T do not merge, signal decision is performed on the basis of the maximum likelihood path at the current time point, i.e., a path with the maximum path metric. The signal decided at this time is delayed from the current time point by a value DT. This value DT is called a decision delay (G. Ungerboeck, "Adaptive maximum-likelihood receiver for carrier-modulated data-transmission systems", IEEE Trans. Commun, vol. COM-22, pp. 624-636, May 1974). Note that D.gtoreq.K.
In this conventional arrangement, since the tap coefficient of the transversal filter 13, i.e., the filter performances, is not updated in a data signal interval of a burst, the performance of the equalizer is degraded in a radio transmission in which the impulse response of the radio transmission varies very fast as in mobile radio communication.
In order to suppress this degradation, attempts have been made to improve the tracking performance with respect to variations in the impulse response of transmission by estimating impulse response of the radio transmission even in a data signal interval of the burst (J. G. Proakis, Digital Communication, McGraw-Hill, 1983). The arrangement for such a technique is shown in FIG. 4.
A quasi-coherent demodulated signal is input to a sampling circuit through an input terminal 40. The sampling circuit 41 outputs a sampled signal y(i). Note that y(i) includes a modulation wave having a symbol period T, and that the sampling period is represented by T.
In a Viterbi algorithm circuit 45, a finite number of state transitions occurs every period T. FIG. 4 shows four types of state transitions. Code sequences corresponding to the respective state transitions are input to a signal generating circuit 47. The signal generating circuit 47 generates complex symbol signal sequences corresponding to the input code sequences. The generated complex symbol signal sequences are sequentially selected by a switch circuit 48 to be input to a transversal filter 410. The input signal sequences, which differ from each other in the respective state transitions, are converted into estimated signals and output by the transversal filter 410, which has a tap coefficient common to all the state transitions. Note that if a complex signal sequence coinciding with a transmitted one is input to the transversal filter 410, an estimated signal nearly equal to the sampled signal is output. The estimated signal is input to a subtracting circuit 42 so that an estimation error is obtained as the difference between the estimated signal and the sampled signal y(i). A squaring circuit 43 calculates the square of the estimation error, multiplies the square by -1, and outputs the resultant value. This value is identified as a branch metric of the state transition selected by a switch circuit 44 and is input to the Viterbi algorithm circuit 45. The Viterbi algorithm circuit 45 performs signal decision and outputs the decision from an output terminal 46. A control circuit 412 estimates and sets the tap coefficient of the transversal filter 410 on the basis of an output from the signal generating circuit 47, which corresponds to the decision, and an output from a delay circuit 411, which receives the sampled signal. In this case, the control circuit 412 corresponds to a control means for setting a priori estimated coefficient vector as the tap coefficient of the transversal filter 410. The delay circuit 411 delays an input signal by a decision delay DT of the Viterbi algorithm circuit 45. Note that D is a positive integer. The switch control circuit 49 controls the switch circuit 44 and a switch circuit 48 at the same timing.
An operation of the control circuit 412 to which a conventional RLS algorithm (to be described later) is applied will be described next. FIG. 5 shows the arrangement of the control circuit 412. A sampled signal delayed by the delay time DT is input through an input terminal 50. A subtracting circuit 51 subtracts a priori estimated signal from the sampled signal and outputs the resultant value as a priori estimation error .alpha..sub.d (i). A multiplying circuit 52 multiplies the error .alpha..sub.d (i) by a gain vector .sub.d (i) and outputs the product as a correction vector. An adding circuit 53 adds the priori estimated coefficient vector and the correction vector together to update a posteriori estimated coefficient vector. A delay circuit 54 delays the posteriori estimated coefficient vector by a time 1T, and outputs it, as the priori estimated coefficient vector, from an output terminal 56, thus setting it as the tap coefficient of the transversal filter 410. Note that this tap coefficient is equivalent to the impulse response of the radio transmission. An inner product operation circuit 55 calculates the inner product of the complex symbol sequence of a decision input from an input terminal 57 and a priori estimated coefficient vector, and outputs the inner product as the priori estimated signal. Note that a gain generating circuit 58 generates Kalman gain vector .sub.d (i) from the complex symbol sequence of the decision. The gain generating circuit 58 consists of an inverse matrix operation circuit 59 and a matrix operation circuit 60. The inverse matrix operation circuit 59 generates an inverse matrix .sub.d (i) (to be described later). The matrix operation circuit 60 multiplies the inverse matrix .sub.d (i) by a vector .sub.d (i) having the decision as an element (to be described later).
The RLS algorithm will be described below.
The complex symbol sequence of the decision from the input terminal 57 is represented by a K-dimensional vector .sub.d (i) as follows: EQU .sup.H.sub.d (i)=[a.sub.d (i-D)a.sub.d (i-D-1) . . . a.sub.d (i-D-K+1)](6)
where a.sub.d (i) is the decision of a(i) and the superscript H denotes Hermitian transposition. A posteriori estimated coefficient vector .sub.d (i) at the time point i is represented by a K-dimensional vector as follows: EQU .sup.H.sub.d (i)=[W*.sub.d (i)W*.sub.d (i-1) . . . W*.sub.d (i-K+1)]. . . (7)
where * denotes complex conjugation and w(i) is the value of the tap coefficient of the transversal filter 410, i.e., the impulse response of the radio transmission. Note that a priori estimated coefficient vector at the time point i is .sub.d (i-1).
In the least squares method, the vector .sub.d (i) is estimated to minimize the weighted square of a posteriori estimation error e.sub.m (i) represented by the following equation: EQU e.sub.d (i)=y(i-D)- .sup.H.sub.d (i) .sub.d (i) (8)
The RLS algorithm is an algorithm for recursively performing this estimation. The following is an algorithm for updating the vector .sub.d (i) (Simon Haykin, "Adaptive Filtering Theory", Prentice-Hall, 1986): ##EQU3## where .sub.d (i) is the inverse matrix of the autocorrelation matrix of .sub.d (i), and k is the forgetting factor positive constant of not more than 1). Note that Kalman gain vector .sub.d (i) is equal to .sub.d (i) .sub.d (i).
In this arrangement, since the impulse response estimation is performed on the basis of a sampled signal delayed by the time DT, the impulse response of the ratio transmission at the time DT past the current time point is estimated. For this reason, the conventional apparatus cannot follow fast ratio transmission variations, in which this delay cannot be neglected, thus causing a degradation in equalization performance.
Furthermore, in the conventional arrangement, when the received signal power level is greatly decreased in a fading environment, a degradation in equalization performances cannot be avoided.
For example, in a TDMA (time division multiple access), a burst having the arrangement shown in FIG. 2 signal for initializing an equalizer, and a subsequent data signal. If the radio transmission is represented by a two-path model with the delay time T, as shown in FIG. 6, two bursts of advanced and delayed paths are weighted by equation (3) and the weighted valves are combined. As a result, the received signal are received with noise added in practice. Therefore, an advanced path at each time point is subjected to intersymbol interference caused by a past symbol delayed by the time T.
A non-minimum phase system in which the level of an advanced path is lower than that of a delayed path will be considered as a case wherein a Viterbi equalizer is not properly operated. FIG. 7 shows a trellis diagram at a last time point N when the burst length is represented by N, provided that EQU .vertline.h.sub.0 .vertline.&lt;.vertline.h.sub.1 .vertline. (10) EQU and EQU y(i)=h.sub.0 a(i)+h.sub.1 a(i-1)+n(i) (11)
If the impulse response of the radio transmission is accurately estimated, a branch metric BR(.sigma..sup.s.sub.N, .sigma..sup.t.sub.N-1) is ##EQU4## In the non-minimum phase, when the level of received signal power is low, the noise level often exceeds .vertline.h.sub.0 .vertline..sup.2. The difference between the symbol and the symbol candidates, represented by a(N)-.alpha.(N), dose not remarkably appear in the branch metrics of two state transitions branching from the same state. That is, in FIG. 7, the branch metrics of state transitions B1 and B2 from a state .sigma..sup.0.sub.N-1 to states .sigma..sup.0.sub.N and .sigma..sup.1.sub.N almost coincide with each other. Similarly, the branch metrics of state transitions B3 and B4 from a state .sigma..sup.1.sub.N-1 to the states .sigma..sup.0.sub.N and .sigma..sup.1.sub.N almost coincide with each other. Therefore, the state transitions B1 and B2 or B3 and B4 are selected. In either case, however, since selected state transition occurs from the same state, there is almost no difference between the branch metrics of the state transitions B1 and B2 or B3 and B4. Consequently, there is no conspicuous difference between path metrics corresponding to the two selected state transitions.
In the conventional equalizer, metric calculation is completed at this time, and a path having the maximum metric is selected to generate a decision signal. Therefore, a decision error is caused at a high probability with respect to the last symbol of a burst. Although the conventional apparatus employs a method of inserting a known signal as the last symbol of a burst in order to eliminate this drawback, a decrease in burst transmission efficiency cannot be avoided because of transmission of known signals.
The relationship between a sampling clock and equalization performance will be described next. FIG. 8 shows the waveform of a received signal having neither waveform distortion nor noise. When the timing offset of the sampling clock is 0, sampling is performed at each time point indicated by "sampling 1". In order to properly operate an equalizer, the received signal waveform must be accurately reproduced from a sampled signal sequence. However, if sampling is performed every symbol interval T, inaccurate waveform reproduction results from a timing offset as will be described below. The received signal waveform shown in FIG. 8 has undergone Nyquist roll-off filtering and contains components having Nyquist frequencies 1/2T to 1/T in a frequency region since the roll-off ratio normally ranges from 0 to 1. Therefore, folded distortion occurs at a Nyquist frequency 1/2T in sampling at every interval T. This distortion varies depending on a sampling timing. This state can be shown by reproducing waveforms based on a sampling function with the sampling period T. FIGS. 9 and 10 respectively show the waveforms at "sampling 1" and "sampling 2". At "sampling 1", the original waveform can be reproduced. However, at "sampling 2", when there is a timing offset T/2, the original waveform cannot be accurately reproduced. In addition, with the timing offset T/2, the average received signal power is reduced.
As described above, in the conventional Viterbi equalizer, since the sampling period coincides with the symbol period, the equalization performance is greatly degraded by the timing offset of the sampling clock.
In the conventional arrangement described above, since the impulse response estimation is performed on the basis of a delayed sampled signal, the past impulse response is estimated. For this reason, the conventional apparatus cannot track fast variations of the impulse response, in which this delay cannot be neglected, thus causing a degradation in equalization performance.
In addition, when the received signal power level is greatly decreased in a fading environment, a degradation in equalization performance cannot be avoided.
Furthermore, a decision error is caused at a high probability with respect to the last symbol of a burst. 10 Although the conventional apparatus employs the method of inserting a known signal as the last symbol of a burst in order to eliminate this drawback, a decrease in burst transmission efficiency cannot be avoided because of transmission of known signals.
Moreover, since the sampling period coincides with the symbol period, the equalization performance is greatly degraded by the timing offset of the sampling clock.